@Jonathan Allin: They are quite different things. In brief once could say that AWS CloudHSM is an IaaS HSM offer for key storage. Customers of AWS (or Azure) could use CloudHSM to host their keys. Azure AD RM is a full information protection SaaS offer that includes an HSM SaaS offer within the broader offer.
Let me know if there was a particular nuance of the question that you're after.